## kenneyfamily 2 years ago Write an equation of the sine function with: amplitude = 7 period = 3π phase shift = π vertical shift = -7

1. Kelumptus

So lets think about what these things mean... Are you familiar with amplitude?

2. kenneyfamily

not really :(

3. Kelumptus

OK, Amplitude is how much to 'amplify' the function by.

4. Kelumptus

or you could say, multiply.

5. Kelumptus

If you have 5Sin(x) then its amplitude is 5 (the wave will hit a maximum of 5 and a minimum of -5.

6. kenneyfamily

ok got it

7. Kelumptus

So hopefully that explains amplitude. The period is the length of a wave before it starts repeating itself. The usual period of a sine function is 2Pi as the wave will begin to repeat after that point in time. I.e. period of Sin(x) is 2Pi. Is this making sense so far?

8. kenneyfamily

so its 7sinx

9. Kelumptus

yep, thats right, 7 sin x (for the amplitude part)

10. UnkleRhaukus

$y(x)=A\sin(\omega t+\phi)+b$ $$A$$ is the Amplitude $$\omega$$ is the angular frequency $$\frac{\omega}{2\pi}=$$frequency of oscillation $$\tau$$ is the period and $$\tau=\frac{2\pi}{\omega}$$ $$\phi$$ is the phase shift $$b$$ is the vertical shift

11. Kelumptus

You are best of taking a look at http://www.intmath.com/trigonometric-graphs/trigo-graph-intro.php. This will explain it properly.